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In a certain game there are 8 steps, referred to as step 1,

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In a certain game there are 8 steps, referred to as step 1, [#permalink] New post 02 Dec 2018, 08:40
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In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Andrea played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Andrea could have gotten?



A. 28

B. 29

C. 30

D. 36

E. 40
[Reveal] Spoiler: OA

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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink] New post 03 Dec 2018, 07:59
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There are 8 slots for the numbers.
Numbers cannot occur consecutively.
We want the greatest sum of the number.
We know this occurs when we have maximum number of 5's
Hence if the number occurred in the following pattern the sum would be greatest
54535251 These digits add to 30
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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink] New post 28 Dec 2018, 04:12
amorphous wrote:
There are 8 slots for the numbers.
Numbers cannot occur consecutively.
We want the greatest sum of the number.
We know this occurs when we have maximum number of 5's
Hence if the number occurred in the following pattern the sum would be greatest
54535251 These digits add to 30


We can also have 54545454. This adds up to 36. Why this is not considered kindly explain.
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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink] New post 28 Dec 2018, 05:13
sumarch2002 wrote:
amorphous wrote:
There are 8 slots for the numbers.
Numbers cannot occur consecutively.
We want the greatest sum of the number.
We know this occurs when we have maximum number of 5's
Hence if the number occurred in the following pattern the sum would be greatest
54535251 These digits add to 30


We can also have 54545454. This adds up to 36. Why this is not considered kindly explain.


This is not possible because 1,2 and 3 should at least feature once
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Post in BookmarksDeleteBookmark [#permalink] New post 28 Dec 2018, 05:31
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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink] New post 28 Dec 2018, 06:21
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There is no need to keep a conversation private.

The forum exists just for this reason: anyone might have benefited from a discussion.

thank you so much
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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink] New post 28 Dec 2018, 08:57
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Carcass wrote:
In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Andrea played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Andrea could have gotten?



A. 28

B. 29

C. 30

D. 36

E. 40



Hi...

The s ores consist of atleast one of each of 1, 2, 3, 4, 5, so 1+2+3+4+5=15 in 5 steps..
Now there are 8-5=3 steps left and let us give them the maximum that is 5, so 15+3*5=30..

We can check for having different score in consecutive steps..
We can have 5,1,5,2,5,3,5,4...1,5,2,5,4,5,3,5.....5,1,2,5,3,5,4 and so on..

C
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
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Re: In a certain game there are 8 steps, referred to as step 1,   [#permalink] 28 Dec 2018, 08:57
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